Highest Common Factor of 85, 67, 66, 30 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 85, 67, 66, 30 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 85, 67, 66, 30 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 85, 67, 66, 30 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 85, 67, 66, 30 is 1.

HCF(85, 67, 66, 30) = 1

HCF of 85, 67, 66, 30 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 85, 67, 66, 30 is 1.

Highest Common Factor of 85,67,66,30 using Euclid's algorithm

Highest Common Factor of 85,67,66,30 is 1

Step 1: Since 85 > 67, we apply the division lemma to 85 and 67, to get

85 = 67 x 1 + 18

Step 2: Since the reminder 67 ≠ 0, we apply division lemma to 18 and 67, to get

67 = 18 x 3 + 13

Step 3: We consider the new divisor 18 and the new remainder 13, and apply the division lemma to get

18 = 13 x 1 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 85 and 67 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(18,13) = HCF(67,18) = HCF(85,67) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 66 > 1, we apply the division lemma to 66 and 1, to get

66 = 1 x 66 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 66 is 1

Notice that 1 = HCF(66,1) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 30 > 1, we apply the division lemma to 30 and 1, to get

30 = 1 x 30 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 30 is 1

Notice that 1 = HCF(30,1) .

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Frequently Asked Questions on HCF of 85, 67, 66, 30 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 85, 67, 66, 30?

Answer: HCF of 85, 67, 66, 30 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 85, 67, 66, 30 using Euclid's Algorithm?

Answer: For arbitrary numbers 85, 67, 66, 30 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.